140 CHAPTER 2. CURVES or −→ p ( θ ) = ( a cos θ,b sin θ ) . To understand the geometric signifcance oF the parameter θ in this case (±igure 2.14 ), imagine a pair oF circles centered at the origin, one circumscribed (with radius the semi-major axis a ), the other inscribed (with radius the semi-minor axis b ) in the ellipse. b a θ ±igure 2.14: Parametrization oF an Ellipse Draw a ray at angle θ with the positive x-axis; the point −→ p ( θ ) is the intersection oF two lines—one vertical, the other horizontal—through the intersections oF the ray with the two circles. Again, the ellipse is
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